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The Stacks project

Definition 73.7.6. Let S be a scheme. A big fppf site (\textit{Spaces}/S)_{fppf} is any site constructed as follows:

  1. Choose a big fppf site (\mathit{Sch}/S)_{fppf} as in Topologies, Section 34.7.

  2. As underlying category take the category \textit{Spaces}/S of algebraic spaces over S (see discussion in Section 73.2 why this is a set).

  3. Choose any set of coverings as in Sets, Lemma 3.11.1 starting with the category \textit{Spaces}/S and the class of fppf coverings of Definition 73.7.1.

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